ESSENTIAL REVISION QUESTIONS. MathsWatch Higher. Book

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1 GCSE Mathematics ESSENTIAL REVISION QUESTIONS MathsWatch Higher Book with answers to all questions enquiries to

2 1T) a) 4t + 7t b) 4t 7t c) 6y + 2w 5y d) 6y 3t e) 4e 2 3e 3 f) m 7 m 5 g) 85 Essential Questions at C to D y y 5 2 (1 to 72 are non-calculator) Grade C Clip 102 a) 11t b) 28t 2 c) y + 2w d) 18yt or 18ty e) 12e 5 f) m 2 g) y 3 h) 3y 3 h) 6y 2y 4 1S) a) 3t + 8t b) 2t 9t c) 12y + 3w 5y d) 4y 2t e) 3e 5 2e 7 f) 4 3 g) r r 7 3 a) 11t b) 18t 2 c) 7y + 3w d) 8yt or 8ty e) 6e 12 f) g) r 4 h) 3r 2 h) 6r 2r 5 3 2T) a) Epand 5(3y 1) b) Epand 3(2 + 4) c) Epand and simplify 2(3 + 5) 3(4 2) d) Epand and simplify 5(2y 3) + 2(y 1) e) (2 + 3)( 4) Grade C Clip 103 2S) a) Epand 3(2y 4) b) Epand 5(3 + 2) c) Epand and simplify 5(2 + 1) 2(3 4) d) Epand and simplify 4(3y 2) + 2(3y 2) e) (3 4)(2 1) a) 15y 5 b) c) d) 12y 17 e) a) 6y 12 b) c) d) 18y 12 e) Page 3 MathsWatch mathswatch@aol.co.uk Page 3

3 5T) Factorise the following: a) b) c) d) e) 2 + f) g) 9h 2 + 6h h) Grade C Clip 104 a) 2( + 3) b) 2( + 4) c) 2( + 6) d) 3( + 2) e) ( + 1) f) 2( 3) g) 3h(3h + 2) h) 2(4 5) 5S) Factorise the following: a) 2t + 10 b) 3m 12 c) 4y + 8 d) e) t 2 + t f) 5t t g) 7t 2 14t h) 9h 2 30h a) 2(t + 5) b) 3(m 4) c) 4(y + 2) d) 2( 2 + 3) e) t(t + 1) f) 5t(t + 2) g) 7t(t 2) h) 3h(3h 10) 6T) a) If a piece of wood is measured as 8cm to the nearest cm, what is the greatest possible length and the least possible length? b) If a piece of wood is measured as 19.8cm to the nearest tenth of a cm, what is the greatest possible length and the least possible length? Grade C Clip 125 6S) a) If a piece of wood is measured as 5cm to the nearest cm, what is the greatest possible length and the least possible length? b) If a piece of wood is measured as 6.7cm to the nearest tenth of a cm, what is the greatest possible length and the least possible length? a) Greatest is 8.5cm Least is 7.5cm b) Greatest is 19.85cm Least is 19.75cm a) Greatest is 5.5cm Least is 4.5cm b) Greatest is 6.75cm Least is 6.65cm Page 5 MathsWatch mathswatch@aol.co.uk Page 5

4 16T) If you share out 240 between Alice and Bill in the ratio 5 : 3, how much more does Alice get compared with Bill? Grade C Clip 94 16S) If you share out 60 between Alice and Bill in the ratio 2 : 3, how much does each of them get? 17T) Sara and Fred share tips from their job in the ratio 2 : 5. If Fred receives 35 how much does Sara get? Grade C Clip 94 17S) Sara and Fred share tips from their job in the ratio 3 : 4. If Sara receives 18 how much does Fred get? for Alice and 36 for Bill T) Some plant heights are measured as shown in the table, below. Height in cm Frequency 0 < h < h < h < h 80 1 a) Find an estimate for the mean height of a plant. b) In which interval does the median height lie? a) 30 b) 20 < h 40 18S) Some plant heights are measured as shown in the table, below. Height in cm Frequency 0 < h < h < h < h 80 3 a) Find an estimate for the mean height of a plant. b) In which interval does the median height lie? Grade C Clip 133 a) 48 b) 40 < h 60 Page 9 MathsWatch mathswatch@aol.co.uk Page 9

5 19T) a) Reflect the shaded shape in the y ais and label it T b) Rotate T 90º anticlockwise using (0, 0) as the centre of rotation and label the new shape U c) Decribe fully the single transformation that will move U back on to the shaded shape. T U c) Reflection in y = Grade D Clips 74, 75, 77 19S) a) Reflect the shaded shape in the ais and label it T b) Rotate T 90º clockwise using (0, 0) as the centre of rotation and label the new shape U c) Decribe fully the single transformation that will move U back on to the shaded shape U T c) Reflection in y = Page 10 MathsWatch mathswatch@aol.co.uk Page 10

6 25T) Solve the following equations a) 2 = 7 b) 8 = 4 c) = 11 d) = 7 e) 2(5 2) = 26 f) 2 3 = 1 5 g) = S) Solve the following equations a) 3 = 12 b) 9 = 3 c) = 14 d) = 4 e) 2(3 + 2) = 46 f) 2 6 = 3 5 g) = 2 3 Grade C Clip 105 a) 3.5 b) 12 c) 4 d) 6 e) 3 f) 5 g) 3.5 a) 4 b) 12 c) 4 d) 6 e) 7 f) 7.5 g) 3 26T) Draw a stem and leaf diagram to show the following information. The heights of 12 plants in cm are: 3.6, 5.2, 4.1, 3.4, 5.8, 6.2, 4.7, 5.2, 4.7, 6.4, 5.1, 4.9 Grade D Clip 89 26S) Draw a stem and leaf diagram to show the following information. The weights of 10 people in kg are: 59, 52, 81, 67, 75, 62, 50, 64, 68, Key 4 1 means Key 6 2 means 62 27T) For each of the following, state whether it is a length, area, volume or none of them (a, b, m, q, r, are lengths) a 2 b 2ab mq r ab(m + q) 2 pr q r 3 Grade C Clip S) For each of the following, state whether it is a length, area, volume or none of them (a, b, m, q, r, are lengths) ab 2ab 2 r 2 + r ab(m + q) pqr 2 r 2 V A L V A A A V A V V L Page 14 MathsWatch mathswatch@aol.co.uk Page 14

7 36T) a) Complete the table for the equation y = Grade C Clip y b) Draw the graph of y = on the aes at the bottom of the page c) Use your graph to find the value of y when = 2.3 d) Use your graph to find the value of y when = 1.5 e) Use your graph to solve = 5 f) Use your graph to solve = 8 c) 3.6 d) 9 e) = 1 and = 2.5 f) = 1.3 and = y O Page 19 MathsWatch mathswatch@aol.co.uk Page 19

8 43T) a) Sketch a scatter diagram with positive correlation hair length, hair colour, intelligence, circumference of wrist, height, ice cream sales, weight, outside temperature sale of etra-warm jackets, eye colour b) From the list above select two sets of data which would have (i) a positive correlation (ii) no correlation Grade D Clip 87 43S) a) Sketch a scatter diagram with negative correlation hair length, hair colour, intelligence, circumference of wrist, height, ice cream sales, weight, outside temperature sale of etra-warm jackets, eye colour b) From the list above select two sets of data which would have (i) a negative correlation (ii) no correlation 44T) a) What are the first four multiples of 7? b) Write down all the factors of 30. c) What are the first si prime numbers? 44S) a) What are the first four multiples of 5? b) Write down all the factors of 40. c) Which two prime numbers come net, after 13? Grade D Clip 44 45T) Solve the inequality < 11 45S) Solve the inequality 5 7 > 43 Grade C Clip T) Evaluate S) Evaluate 2 4 Grade D Clip 45 a) b) (i) height and weight or Ice cream sales and temp. (ii) hair length and hair colour or hair colour and intelligence etc a) b) (i) temp. and sale of jackets (ii) eye colour and intelligence or hair length and weight etc a) b) c) a) b) c) < 4 > Page 24 MathsWatch mathswatch@aol.co.uk Page 24

9 Questions 73 to 85 are all calculator questions 73T) Find the length of sides A, B and C giving your answers to one decimal place. 14cm A 13.9cm 12cm A 23cm B B C 18.2cm 5.6cm 7cm Grade C Clip 118 C 3.9cm 6.8cm 73S) Find the length of sides A, B and C giving your answers to one decimal place. A 17cm 126cm 58cm A B C 14.4cm 111.9cm 12.7cm 9cm B 9.5cm 8.5cm C 74T) The equation = 20 has a solution between 2 and 3. Use a trial and improvement method to find this solution. Give your answer to 1 decimal place and show all workings. 74S) The equation 3 4 = 88 has a solution between 4 and 5. Use a trial and improvement method to find this solution. Give your answer to 1 decimal place and show all workings. Grade D Clip 110 = = 12 Too low = = 33 Too big = = Too low = = Too big = = Too low = 2.5 to 1 decimal place. = = 48 Too low = = 105 Too big = = Too low = = Too big = = Too big = 4.7 to 1 decimal place. Page 35 MathsWatch mathswatch@aol.co.uk Page 35

10 22 Essential Questions at grade B (A calculator can be used on all questions apart from qu. 13) 1T) Solve these two simultaneous equations 2r + 3s = 6 3r 2s = 22 Grade B Clip 142 1S) Solve these two simultaneous equations h + 3t = 10 2h t = 8 r = 6 and s = 2 h = 2 and t = 4 2T) Mary recorded the heights, in centimetres, of the girls in her class. She put the heights in order Grade B Clip 152 a) LQ = 152 b) UQ = 177 a) Find the lower quartile b) Find the upper quartile c) On the grid, draw a boplot for this data. 2S) Mary recorded the heights, in centimetres, of the girls in her class. She put the heights in order. a) LQ = 154 b) UQ = a) Find the lower quartile b) Find the upper quartile c) On the grid, draw a boplot for this data. Page 41 MathsWatch mathswatch@aol.co.uk Page 41

11 8T) The heights of 64 plants were measured and can be seen in this table. Height (cm) Frequency Grade B Clip < h < < h < < h < < h < < h < < h < 60 2 a) Complete this cumulative frequency table. a) CF Height (cm) Cumulative Frequency 0 < h < < h < 20 0 < h < 30 0 < h < 40 0 < h < 50 0 < h < 60 b) Draw a cumulative frequency curve for your table. c) Use your graph to find an estimate for the b) 80 interquartile range of the heights of the plants. CF Height (cm) Cumulative Frequency 0 < h < < h < < h < < h < < h < < h < UQ median LQ c) IR = UQ LQ = = 11cm Height (cm) Height (cm) Page 45 MathsWatch mathswatch@aol.co.uk Page 45

12 21T) a) A straight line is parallel to y = 3 1 and goes through (1, 7). What is its equation? b) A straight line goes through points (1, 5) and (3, 13). What is its equation? Grade B Clip S) a) A straight line is parallel to y = 5 3 and goes through (3, 17). What is its equation? b) A straight line goes through points (1, 5) and (3, 3). What is its equation? a) y = b) y = a) y = b) y = 6 22T) Sketch the graphs of a) y = 2 b) y = 3 c) y = d) y = - 3 Grade B Clip S) Sketch the graphs of a) y = - 2 b) y = c) y = 3 6 d) y = 2 4 y = 2 y = 3 a) b) 1 y = c) d) 4 y = - 3 y = - 2 y = a) b) 1 c) y = 3 6 d) y = Page 53 MathsWatch mathswatch@aol.co.uk Page 53

13 26 Essential Questions at grade A/A* (A calculator can be used on all questions unless told otherwise) 1T) y (2, 1) y = f() Grade A/A* Clip The diagram shows part of the curve with equation y = f(). The coordinates of the maimum point of this curve are (2, 1). Write down the coordinates of the maimum point of the curve with equation a) y = f() + 3 b) y = f() 1 c) y = f( 3) d) y = 2f() e) y = f(½) a) (2, 4) b) (2, 0) c) (5, 1) d) (2, 2) e) (4, 1) 1S) y y = f() 0 (1, -4) The diagram shows part of the curve with equation y = f(). The coordinates of the minimum point of this curve are (1, -4). Write down the coordinates of the minimum point of the curve with equation a) y = ½f() b) y = f(2) c) y = f( + 5) d) y = f() + 4 e) y = 3f() a) (1, -2) b) (0.5, -4) c) (-4, -4) d) (1, 0) e) (1, -12) Page 55 MathsWatch mathswatch@aol.co.uk Page 55

14 2T) For each triangle find the side or angle marked with the letter. Give your answer correct to 1 decimal place. a) b) 8 cm Grade A/A* Clip cm cm a) 6.3 cm b) 40.6 c) 11.7 cm c) d) 6 cm d) cm cm 5 cm 7 cm 2S) For each triangle find the side or angle marked with the letter. Give your answer correct to 1 decimal place. 62 a) b) m 12 m 5 cm 14m c) d)* 8 cm 7 cm cm a) 78.5 b) 5.2 cm c) 10.0 cm d) cm *A tricky sine rule question. 3T) Solve = 0 Give your solutions correct to 2 decimal places. 3S) Solve = 0 Give your solutions correct to 2 decimal places. Grade A/A* Clip 161 = 1.15 or = = 2.28 or = 0.22 Page 56 MathsWatch mathswatch@aol.co.uk Page 56

15 15S) This histogram gives information about the paintings sold in a shop one Saturday. Frequency density Price (P) in pounds ( ) a) Use the histogram to complete the table. Price (p) in pounds ( ) Frequency 0 < p < 5 5 < p < < p < < p < 40 0 < p < 5 5 < p < < p < < p < This table gives information about the paintings sold in another shop on the same Saturday. Price (p) in pounds ( ) Frequency 0 < p < 5 5 < p < < p < < p < b) Draw a histogram to represent this information. Frequency density Price (p) in pounds ( ) Page 64 MathsWatch mathswatch@aol.co.uk Page 64

16 24T) H G E F D 16 cm C 8 cm A 9 cm B This is a cuboid, ABCDEFGH AB = 9 cm, BC = 8 cm, AG = 16 cm 24S) a) Calculate the length AE. Give your answer to 3 significant figures. b) Work out the angle between CE and the horizontal plane ABCD. Give your answer to 2 significant figures. Grade A/A* Clips 174 and 175 X a) 10.5 cm b) 41º D C 12 cm M 9 cm A 9 cm B The diagram shows a square-based pyramid ABCDX. AB = BC = 9 cm. The point M is the centre of the square base. XM = 12 cm. a) Calculate the length of AC. Give your answer to 3 significant figures. b) Work out the angle between the edge AX and the horizontal plane ABCD. Give your answer to 1 decimal place. a) 12.7 cm b) 62.1º Page 70 MathsWatch mathswatch@aol.co.uk Page 70